(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 10.4' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[     15289,        562]
NotebookOptionsPosition[     10543,        403]
NotebookOutlinePosition[     13593,        495]
CellTagsIndexPosition[     13485,        489]
WindowTitle->SumP
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[GridBox[{
   {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{
     Cell[BoxData[
      ActionMenuBox[
       FrameBox[
        InterpretationBox[Cell[TextData[{
          "See Also",
          StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow",
           StripOnInput->False]
         }]],
         TextCell[
          Row[{"See Also", 
            Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]],
        StripOnInput->False], {"\<\"SumS\"\>":>Documentation`HelpLookup[
       "paclet:FeynCalc/ref/SumS"], "\<\"SumT\"\>":>Documentation`HelpLookup[
       "paclet:FeynCalc/ref/SumT"]},
       Appearance->None,
       MenuAppearance->Automatic,
       MenuStyle->"SeeAlso"]],
      LineSpacing->{1.4, 0}],
     "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\
\[ThickSpace]",
     Cell[BoxData[
      ActionMenuBox[
       FrameBox[
        InterpretationBox[Cell[TextData[{
          "URL",
          StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow",
           StripOnInput->False]
         }]],
         TextCell[
          Row[{"URL", 
            Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]],
        StripOnInput->False], {"\<\"FeynCalc/ref/SumP\"\>":>
       None, "\<\"Copy Wolfram Documentation Center URL\"\>":>
       Module[{DocumentationSearch`Private`nb$}, 
        DocumentationSearch`Private`nb$ = NotebookPut[
           Notebook[{
             Cell["FeynCalc/ref/SumP"]}, Visible -> False]]; 
        SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; 
        FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; 
        NotebookClose[DocumentationSearch`Private`nb$]; Null], 
       Delimiter, "\<\"Copy web URL\"\>":>
       Module[{DocumentationSearch`Private`nb$}, 
        DocumentationSearch`Private`nb$ = NotebookPut[
           Notebook[{
             Cell[
              BoxData[
               MakeBoxes[
                Hyperlink[
                "http://reference.wolfram.com/language/FeynCalc/ref/SumP.\
html"], StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> 
            False]]; SelectionMove[
         DocumentationSearch`Private`nb$, All, Notebook]; 
        FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; 
        NotebookClose[DocumentationSearch`Private`nb$]; 
        Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{
         NotebookLocate[{
           URL[
            StringJoin[
             If[
              TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$254373], 
              "http://reference.wolfram.com/system-modeler/", 
              "http://reference.wolfram.com/language/"], "FeynCalc/ref/SumP", 
             ".html"]], None}]}]},
       Appearance->None,
       MenuAppearance->Automatic,
       MenuStyle->"URLMenu"]],
      LineSpacing->{1.4, 0}]
    }], "AnchorBar"]}
  }]], "AnchorBarGrid",
 GridBoxOptions->{GridBoxItemSize->{"Columns" -> {
     Scaled[0.65], {
      Scaled[0.34]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
   "RowsIndexed" -> {}}},
 CellID->1],

Cell[TextData[{
 Cell["SumP", "ObjectName"],
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{8, 0}],
    CacheGraphics->False],
   Spacer[8]]]],
 Cell[BoxData[""], "ObjectNameTranslation"]
}], "ObjectNameGrid"],

Cell[BoxData[GridBox[{
   {"", Cell[TextData[{
     Cell[BoxData[
      RowBox[{"SumP", "[", 
       RowBox[{"k", ",", " ", "m"}], "]"}]], "InlineFormula"],
     " \[LineSeparator]",
     "is ",
     Cell[BoxData[
      FormBox[
       RowBox[{
        SuperscriptBox["2", 
         RowBox[{
          StyleBox["k",
           FontSlant->"Plain"], "-", "1"}]], 
        RowBox[{
         SubsuperscriptBox["\[Sum]", 
          RowBox[{
           StyleBox["i",
            FontSlant->"Plain"], "=", "1"}], 
          RowBox[{"2", 
           StyleBox["m",
            FontSlant->"Plain"]}]], 
         RowBox[{
          RowBox[{"(", 
           RowBox[{"1", "+", 
            SuperscriptBox[
             RowBox[{"(", 
              RowBox[{"-", "1"}], ")"}], 
             StyleBox["i",
              FontSlant->"Plain"]]}], ")"}], "/", 
          SuperscriptBox[
           StyleBox["i",
            FontSlant->"Plain"], 
           StyleBox["k",
            FontSlant->"Plain"]]}]}]}], TraditionalForm]]]
    }]]}
  }]], "Usage",
 GridBoxOptions->{
 GridBoxBackground->{
  "Columns" -> {{None}}, "ColumnsIndexed" -> {}, "Rows" -> {{None}}, 
   "RowsIndexed" -> {}}},
 CellID->982511436],

Cell[CellGroupData[{

Cell[TextData[{
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{6, 0}],
    CacheGraphics->False],
   Spacer[6]]]],
 "Examples",
 "\[NonBreakingSpace]\[NonBreakingSpace]",
 Cell["(1)", "ExampleCount"]
}], "PrimaryExamplesSection",
 WholeCellGroupOpener->True,
 CellTags->"PrimaryExamplesSection",
 CellID->295016219],

Cell[CellGroupData[{

Cell[TextData[{
 "Basic Examples",
 "\[NonBreakingSpace]\[NonBreakingSpace]",
 Cell["(1)", "ExampleCount"]
}], "ExampleSection", "ExampleSection",
 WholeCellGroupOpener->True,
 CellID->587251090],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"SumP", "[", 
  RowBox[{"1", ",", 
   RowBox[{"m", "-", "1"}]}], "]"}]], "Input",
 CellTags->"SumP",
 CellLabel->"In[1]:=",
 CellID->2064705419],

Cell[BoxData[
 FormBox[
  RowBox[{
   SubsuperscriptBox["S", "1", "'"], "\[NoBreak]", "(", "\[NoBreak]", 
   FormBox[
    RowBox[{"m", "-", "1"}],
    TraditionalForm], "\[NoBreak]", ")"}], TraditionalForm]], "Output",
 ImageSize->{72, 18},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"SumP",
 CellLabel->"Out[1]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"SumP", "[", 
  RowBox[{"2", ",", 
   RowBox[{"m", "-", "1"}]}], "]"}]], "Input",
 CellTags->"SumP",
 CellLabel->"In[2]:=",
 CellID->1846990318],

Cell[BoxData[
 FormBox[
  RowBox[{
   SubsuperscriptBox["S", "2", "'"], "\[NoBreak]", "(", "\[NoBreak]", 
   FormBox[
    RowBox[{"m", "-", "1"}],
    TraditionalForm], "\[NoBreak]", ")"}], TraditionalForm]], "Output",
 ImageSize->{72, 17},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"SumP",
 CellLabel->"Out[2]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"SumP", "[", 
  RowBox[{"1", ",", "m"}], "]"}]], "Input",
 CellTags->"SumP",
 CellLabel->"In[3]:=",
 CellID->1164731188],

Cell[BoxData[
 FormBox[
  RowBox[{
   SubsuperscriptBox["S", "1", "'"], "\[NoBreak]", "(", "\[NoBreak]", 
   FormBox["m",
    TraditionalForm], "\[NoBreak]", ")"}], TraditionalForm]], "Output",
 ImageSize->{49, 18},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"SumP",
 CellLabel->"Out[3]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"SumP", "[", 
  RowBox[{"1", ",", "4"}], "]"}]], "Input",
 CellTags->"SumP",
 CellLabel->"In[4]:=",
 CellID->1167358521],

Cell[BoxData[
 FormBox[
  FractionBox["25", "12"], TraditionalForm]], "Output",
 ImageSize->{23, 35},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"SumP",
 CellLabel->"Out[4]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  UnderoverscriptBox["\[Sum]", 
   RowBox[{"i", "=", "1"}], "8"], 
  RowBox[{
   RowBox[{"(", 
    RowBox[{"1", "+", 
     RowBox[{
      RowBox[{"(", 
       RowBox[{"-", "1"}], ")"}], "^", "i"}]}], ")"}], "/", "i"}]}]], "Input",\

 CellTags->"SumP",
 CellLabel->"In[5]:=",
 CellID->1893183879],

Cell[BoxData[
 FormBox[
  FractionBox["25", "12"], TraditionalForm]], "Output",
 ImageSize->{23, 35},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"SumP",
 CellLabel->"Out[5]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Explicit", "[", 
  RowBox[{"SumP", "[", 
   RowBox[{"1", ",", 
    RowBox[{"n", "/", "2"}]}], "]"}], "]"}]], "Input",
 CellTags->"SumP",
 CellLabel->"In[6]:=",
 CellID->1686985952],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    FractionBox["1", "2"], " ", 
    RowBox[{"(", 
     RowBox[{
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"-", "1"}], ")"}], 
       RowBox[{"n", "+", "1"}]], "+", "1"}], ")"}], " ", 
    RowBox[{
     SubscriptBox["S", "1"], "(", 
     FormBox[
      FractionBox[
       RowBox[{"n", "-", "1"}], "2"],
      TraditionalForm], ")"}]}], "+", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    RowBox[{"(", 
     RowBox[{
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"-", "1"}], ")"}], "n"], "+", "1"}], ")"}], " ", 
    RowBox[{
     SubscriptBox["S", "1"], "(", 
     FormBox[
      FractionBox["n", "2"],
      TraditionalForm], ")"}]}]}], TraditionalForm]], "Output",
 ImageSize->{335, 36},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"SumP",
 CellLabel->"Out[6]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"%", "/.", 
  RowBox[{"n", "\[Rule]", "8"}]}]], "Input",
 CellTags->"SumP",
 CellLabel->"In[7]:=",
 CellID->1663422834],

Cell[BoxData[
 FormBox[
  FractionBox["25", "12"], TraditionalForm]], "Output",
 ImageSize->{23, 35},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"SumP",
 CellLabel->"Out[7]="]
}, Open  ]]
}, Open  ]],

Cell["", "SectionFooterSpacer"]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{6, 0}],
    CacheGraphics->False],
   Spacer[6]]]],
 "See Also"
}], "SeeAlsoSection",
 WholeCellGroupOpener->True,
 CellID->1255426704],

Cell[TextData[{
 StyleBox[ButtonBox["SumS",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/SumS",
  ButtonNote->"SumS"],
  FontFamily->"Verdana"],
 ", ",
 StyleBox[ButtonBox["SumT",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/SumT",
  ButtonNote->"SumT"],
  FontFamily->"Verdana"],
 "."
}], "SeeAlso"]
}, Open  ]],

Cell[" ", "FooterCell"]
},
Saveable->False,
ScreenStyleEnvironment->"Working",
WindowSize->{725, 750},
WindowMargins->{{-10, Automatic}, {Automatic, -8}},
WindowTitle->"SumP",
TaggingRules->{
 "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> 
  GridBox[{{
      RowBox[{
        ButtonBox[
        "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", 
         BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> 
    Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> 
  None, "RootCaptions" -> "", 
  "Metadata" -> {
   "built" -> "{2020, 6, 20, 19, 11, 15.577451}", 
    "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", 
    "keywords" -> {}, "specialkeywords" -> {}, 
    "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> 
    "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> 
    "None", "summary" -> 
    "SumP[k, m] is 2 k - 1 \\[Sum]_i = 1^2 m(1 + (-1) i)/i^k", 
    "synonyms" -> {}, "tabletags" -> {}, "title" -> "SumP", "titlemodifier" -> 
    "", "windowtitle" -> "SumP", "type" -> "Symbol", "uri" -> 
    "FeynCalc/ref/SumP"}, "SearchTextTranslated" -> ""},
CellContext->"Global`",
FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)",
StyleDefinitions->Notebook[{
   Cell[
    StyleData[
    StyleDefinitions -> FrontEnd`FileName[{"Wolfram"}, "Reference.nb"]]], 
   Cell[
    StyleData["Input"], CellContext -> "Global`"], 
   Cell[
    StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, 
  FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", 
  StyleDefinitions -> "Default.nb"]
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{
 "PrimaryExamplesSection"->{
  Cell[5134, 156, 387, 15, 31, "PrimaryExamplesSection",
   CellTags->"PrimaryExamplesSection",
   CellID->295016219]},
 "SumP"->{
  Cell[5766, 185, 167, 6, 27, "Input",
   CellTags->"SumP",
   CellID->2064705419],
  Cell[5936, 193, 347, 11, 39, "Output",
   CellTags->"SumP"],
  Cell[6320, 209, 167, 6, 27, "Input",
   CellTags->"SumP",
   CellID->1846990318],
  Cell[6490, 217, 347, 11, 38, "Output",
   CellTags->"SumP"],
  Cell[6874, 233, 143, 5, 27, "Input",
   CellTags->"SumP",
   CellID->1164731188],
  Cell[7020, 240, 322, 10, 39, "Output",
   CellTags->"SumP"],
  Cell[7379, 255, 143, 5, 27, "Input",
   CellTags->"SumP",
   CellID->1167358521],
  Cell[7525, 262, 208, 7, 56, "Output",
   CellTags->"SumP"],
  Cell[7770, 274, 319, 13, 58, "Input",
   CellTags->"SumP",
   CellID->1893183879],
  Cell[8092, 289, 208, 7, 56, "Output",
   CellTags->"SumP"],
  Cell[8337, 301, 204, 7, 27, "Input",
   CellTags->"SumP",
   CellID->1686985952],
  Cell[8544, 310, 877, 33, 57, "Output",
   CellTags->"SumP"],
  Cell[9458, 348, 142, 5, 27, "Input",
   CellTags->"SumP",
   CellID->1663422834],
  Cell[9603, 355, 208, 7, 56, "Output",
   CellTags->"SumP"]}
 }
*)
(*CellTagsIndex
CellTagsIndex->{
 {"PrimaryExamplesSection", 12303, 446},
 {"SumP", 12434, 450}
 }
*)
(*NotebookFileOutline
Notebook[{
Cell[576, 21, 3056, 75, 53, "AnchorBarGrid",
 CellID->1],
Cell[3635, 98, 281, 11, 45, "ObjectNameGrid"],
Cell[3919, 111, 1190, 41, 93, "Usage",
 CellID->982511436],
Cell[CellGroupData[{
Cell[5134, 156, 387, 15, 31, "PrimaryExamplesSection",
 CellTags->"PrimaryExamplesSection",
 CellID->295016219],
Cell[CellGroupData[{
Cell[5546, 175, 195, 6, 26, "ExampleSection",
 CellID->587251090],
Cell[CellGroupData[{
Cell[5766, 185, 167, 6, 27, "Input",
 CellTags->"SumP",
 CellID->2064705419],
Cell[5936, 193, 347, 11, 39, "Output",
 CellTags->"SumP"]
}, Open  ]],
Cell[CellGroupData[{
Cell[6320, 209, 167, 6, 27, "Input",
 CellTags->"SumP",
 CellID->1846990318],
Cell[6490, 217, 347, 11, 38, "Output",
 CellTags->"SumP"]
}, Open  ]],
Cell[CellGroupData[{
Cell[6874, 233, 143, 5, 27, "Input",
 CellTags->"SumP",
 CellID->1164731188],
Cell[7020, 240, 322, 10, 39, "Output",
 CellTags->"SumP"]
}, Open  ]],
Cell[CellGroupData[{
Cell[7379, 255, 143, 5, 27, "Input",
 CellTags->"SumP",
 CellID->1167358521],
Cell[7525, 262, 208, 7, 56, "Output",
 CellTags->"SumP"]
}, Open  ]],
Cell[CellGroupData[{
Cell[7770, 274, 319, 13, 58, "Input",
 CellTags->"SumP",
 CellID->1893183879],
Cell[8092, 289, 208, 7, 56, "Output",
 CellTags->"SumP"]
}, Open  ]],
Cell[CellGroupData[{
Cell[8337, 301, 204, 7, 27, "Input",
 CellTags->"SumP",
 CellID->1686985952],
Cell[8544, 310, 877, 33, 57, "Output",
 CellTags->"SumP"]
}, Open  ]],
Cell[CellGroupData[{
Cell[9458, 348, 142, 5, 27, "Input",
 CellTags->"SumP",
 CellID->1663422834],
Cell[9603, 355, 208, 7, 56, "Output",
 CellTags->"SumP"]
}, Open  ]]
}, Open  ]],
Cell[9838, 366, 31, 0, 29, "SectionFooterSpacer"]
}, Open  ]],
Cell[CellGroupData[{
Cell[9906, 371, 270, 12, 31, "SeeAlsoSection",
 CellID->1255426704],
Cell[10179, 385, 322, 13, 56, "SeeAlso"]
}, Open  ]],
Cell[10516, 401, 23, 0, 41, "FooterCell"]
}
]
*)

(* End of internal cache information *)

